We derive an algorithm based on the fast Fourier transform to construct a real symmetric matrix S with eigenvalues λ1 ≥ λ2 ≥ ⋯ ≥ λn, with eigenvector e = [1,1,..., 1]T belonging to the eigenvalue λ1. We find simple conditions on the eigenvalues such that the algorithm constructs an irreducible matrix S = λ1E, where E is a symmetric doubly stochastic matrix. © 2003 Elsevier Science Ltd. All rights reserved.
Rojo, O., & Rojo, H. (2003). Constructing symmetric nonnegative matrices via the fast Fourier transform. Computers and Mathematics with Applications, 45(10–11), 1655–1672. https://doi.org/10.1016/S0898-1221(03)00145-7